Draw a 3D Parametric Plot
Plot a two-parameter surface in three dimensions.
parametric3d(fx, fy, fz, u, v, umin, umax, vmin, vmax, n = 100,
color = "white", color2 = NA, alpha = 1,
fill = TRUE, col.mesh = if (fill) NA else color,
smooth = 0, material = "default",
add = FALSE, draw = TRUE, engine = "rgl", ...)fx,fy,fz |
vectorized functions of u and v to compute the
|
u |
numeric vector of u values. |
v |
numeric vector of v values. |
umin |
numeric; the minimum value of u. Ignored if |
umax |
numeric; the maximum value of u. Ignored if |
vmin |
numeric; the minimum value of v. Ignored if |
vmax |
numeric; the maximum value of v. Ignored if |
n |
the number of equally spaced |
color |
color to use for the surface. Can also be a function of three arguments. This is called with three arguments, the coordinates of the midpoints of the triangles making up the surface. The function should return a vector of colors to use for the triangles. |
color2 |
opposite face color. |
alpha |
alpha channel level, a number between 0 and 1.. |
fill |
logical; if |
col.mesh |
color to use for the wire frame. |
smooth |
integer or logical specifying Phong shading level for "standard" and "grid" engines or whether or not to use shading for the "rgl" engine. |
material |
material specification; currently only used by "standard" and "grid" engines. Currently possible values are the character strings "dull", "shiny", "metal", and "default". |
add |
logical; if |
draw |
logical; if |
engine |
character; currently "rgl", "standard", "grid" or "none"; for "none" the computed triangles are returned. |
... |
additional rendering arguments, e.g. material and texture
properties for the "rgl" engine. See documentation for
|
Analogous to Mathematica's Param3D. Evaluates the
functions fx, fy, and fz specifying the
coordinates of the surface at a grid of values for the
parameters u and v.
For the "rgl" engine the returned value is NULL. For the
"standard" and "grid" engines the returned value is the viewing
transformation as returned by persp. For the engine "none", or
when draw is not true, the returned value is a structure
representing the triangles making up the surface.
The "rgl" engine now uses the standard rgl coordinates instead of
negating y and swapping y and z. If you need to
reproduce the previous behavior you can use
options(old.misc3d.orientation=TRUE).
Transparency only works properly in the "rgl" engine. For standard or grid graphics on pdf or quartz devices using alpha levels less than 1 does work but the triangle borders show as a less transparent mesh.
Daniel Adler, Oleg Nenadic and Walter Zucchini (2003) RGL: A R-library for 3D visualization with OpenGL
#Example 1: Ratio-of-Uniform sampling region of bivariate normal
parametric3d(fx = function(u, v) u * exp(-0.5 * (u^2 + v^2 -
2 * 0.75 * u * v)/sqrt(1-.75^2))^(1/3),
fy = function(u, v) v * exp(-0.5 * (u^2 + v^2 -
2 * 0.75 * u * v)/sqrt(1-.75^2))^(1/3),
fz = function(u, v) exp(-0.5 * (u^2 + v^2 - 2 * 0.75 * u *
v)/sqrt(1-.75^2))^(1/3),
umin = -20, umax = 20, vmin = -20, vmax = 20,
n = 100)
parametric3d(fx = function(u, v) u * exp(-0.5 * (u^2 + v^2 -
2 * 0.75 * u * v)/sqrt(1-.75^2))^(1/3),
fy = function(u, v) v * exp(-0.5 * (u^2 + v^2 -
2 * 0.75 * u * v)/sqrt(1-.75^2))^(1/3),
fz = function(u, v) exp(-0.5 * (u^2 + v^2 - 2 * 0.75 * u *
v)/sqrt(1-.75^2))^(1/3),
u = qcauchy((1:100)/101), v = qcauchy((1:100)/101))
parametric3d(fx = function(u, v) u * exp(-0.5 * (u^2 + v^2 -
2 * 0.75 * u * v)/sqrt(1-.75^2))^(1/3),
fy = function(u, v) v * exp(-0.5 * (u^2 + v^2 -
2 * 0.75 * u * v)/sqrt(1-.75^2))^(1/3),
fz = function(u, v) exp(-0.5 * (u^2 + v^2 - 2 * 0.75 * u *
v)/sqrt(1-.75^2))^(1/3),
u = qcauchy((1:100)/101), v = qcauchy((1:100)/101),
engine = "standard", scale = FALSE, screen = list(x=-90, y=20))
#Example 2: Ratio-of-Uniform sampling region of Bivariate t
parametric3d(fx = function(u,v) u*(dt(u,2) * dt(v,2))^(1/3),
fy = function(u,v) v*(dt(u,2) * dt(v,2))^(1/3),
fz = function(u,v) (dt(u,2) * dt(v,2))^(1/3),
umin = -20, umax = 20, vmin = -20, vmax = 20,
n = 100, color = "green")
parametric3d(fx = function(u,v) u*(dt(u,2) * dt(v,2))^(1/3),
fy = function(u,v) v*(dt(u,2) * dt(v,2))^(1/3),
fz = function(u,v) (dt(u,2) * dt(v,2))^(1/3),
u = qcauchy((1:100)/101), v = qcauchy((1:100)/101),
color = "green")
parametric3d(fx = function(u,v) u*(dt(u,2) * dt(v,2))^(1/3),
fy = function(u,v) v*(dt(u,2) * dt(v,2))^(1/3),
fz = function(u,v) (dt(u,2) * dt(v,2))^(1/3),
u = qcauchy((1:100)/101), v = qcauchy((1:100)/101),
color = "green", engine = "standard", scale = FALSE)
#Example 3: Surface of revolution
parametric3d(fx = function(u,v) u,
fy = function(u,v) sin(v)*(u^3+2*u^2-2*u+2)/5,
fz = function(u,v) cos(v)*(u^3+2*u^2-2*u+2)/5,
umin = -2.3, umax = 1.3, vmin = 0, vmax = 2*pi)
parametric3d(fx = function(u,v) u,
fy = function(u,v) sin(v)*(u^3+2*u^2-2*u+2)/5,
fz = function(u,v) cos(v)*(u^3+2*u^2-2*u+2)/5,
umin = -2.3, umax = 1.3, vmin = 0, vmax = 2*pi,
engine = "standard", scale = FALSE,
color = "red", color2 = "blue", material = "shiny")Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.